Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10:
ISBN 13:

Chapter 3 - Adding and Subtracting Fractions - 3.4 Adding and Subtracting Mixed Numbers - 3.4 Exercises - Page 228: 25

Answer

Estimated answer = 12 Exact answer = $11\frac{7}{15}$

Work Step by Step

$12\frac{2}{3}$ - $1\frac{1}{5}$ Estimation: $12\frac{2}{3} \approx 13$ $1\frac{1}{5} \approx 1$ Therefore $12\frac{2}{3}$ - $1\frac{1}{5}$ $\approx$ 13 - 1 = 12 Exact Calculation: $12\frac{2}{3}$ - $1\frac{1}{5}$ = $12\frac{2\times5}{3\times5}$ - $1\frac{1\times3}{5\times3}$ (15 is the least common denominator) = $12\frac{10}{15}$ - $1\frac{3}{15}$ = $12$ + $\frac{10}{15}$ - ($1$ + $\frac{3}{15})$ = $12$ + $\frac{10}{15}$ - $1$ - $\frac{3}{15}$ = ($12$ - $1$) + ($\frac{10}{15}$ - $\frac{3}{15}$) (Solving whole parts separately and fractional parts separately) = $11$ + $\frac{10 - 3}{15}$ = $11$ + $\frac{7}{15}$ = $11\frac{7}{15}$ The estimate was 12, so the exact answer of $11\frac{7}{15}$ is reasonable.
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